You know, I'm leaning towards not fixing what's not broken. It might not be hip or sexy, but for this application SSI has much to recommend it.

Zero learning curve

already installed, ready to go, proven, stable

No more resource hungry than a templating system

While it does use resources each page serve, this is a low-traffic site on a private server that won't even notice the minor load

Although it is static, the content and the nav bar do change from time to time. An off-line generator would mean having to re-generate the entire website each time any page was updated, adding steps of complexity in a a situation where pages may be edited by multiple authors who have limited web skills to being with. Or I have to develop an interface for that function too. Whereas with SSI, edit the file directly once, and that's it, done.